Plate Buckling in the Strain-Hardening Range

The application of plastic design to continuous frames constructed of wide-flange shapes imposes more severe limitations on the geometry of these shapes than does conventional elastic design. In regions in which yielding begin-first, the flanges must be able to sustain strains considerably larger than the yield strain without the occurrence of local (plate) buckling. With this practical application in mind, the problem of buckling of steel plates compressed beyond the yield strain is treated herein. In the strains hardening range the material is considered to be homogeneous. However, because of the yielding process, the material cannot be expected to remain isotropic. Therefore, general expressions for the buckling strength are derived, assuming that the material has become orthogonally anisotropic. Orthogonal anisotropy in the case of plane stress is expressed mathematically by stress-strain relationships involving five moduli. Numerical values of the moduli are estimated from the incremental theory of plasticity, using the second invariant of the deviatoric stress tensor as the loading function. The influence of initial imperfections is taken into account through proper adjustment of the values of the moduli. For the selection of these values, due consideration is given to the results of buckling tests. In the yielding range, the average strain in the direction of loading is between the strain at which yielding begins and the strain at which strain hardening commences. For this case the material is considered to be partly elastic and partly strained up to the strain-hardening range. Finally, theoretical estimates are compared with test results. It is considered that the theory adequately describes the behavior.